Replays of spatial memories suppress topological fluctuations in cognitive map

Topological data analysis of the firings of a network of stochastic spiking neurons

Topological data analysis is becoming more and more popular in recent years. It has found various applications in many different fields, for its convenience in analyzing and understanding the structure and dynamic of complex systems. We used topological data analysis to analyze the firings of a network of stochastic spiking neurons, which can be in a sub-critical, critical, or super-critical state depending on the value of the control parameter. We calculated several topological features regarding Betti curves and then analyzed the behaviors of these features, using them as inputs for machine learning to discriminate the three states of the network.

Efficient, continual, and generalized learning in the brain - neural mechanism of Mental Schema 2.0

There has been tremendous progress in artificial neural networks (ANNs) over the past decade; however, the gap between ANNs and the biological brain as a learning device remains large. With the goal of closing this gap, this paper reviews learning mechanisms in the brain by focusing on three important issues in ANN research: efficiency, continuity, and generalization. We first discuss the method by which the brain utilizes a variety of self-organizing mechanisms to maximize learning efficiency, with a focus on the role of spontaneous activity of the brain in shaping synaptic connections to facilitate spatiotemporal learning and numerical processing. Then, we examined the neuronal mechanisms that enable lifelong continual learning, with a focus on memory replay during sleep and its implementation in brain-inspired ANNs. Finally, we explored the method by which the brain generalizes learned knowledge in new situations, particularly from the mathematical generalization perspective of topology. Besides a systematic comparison in learning mechanisms between the brain and ANNs, we propose "Mental Schema 2.0," a new computational property underlying the brain's unique learning ability that can be implemented in ANNs.

Pattern dynamics and stochasticity of the brain rhythms

Our current understanding of brain rhythms is based on quantifying their instantaneous or time-averaged characteristics. What remains unexplored is the actual structure of the waves-their shapes and patterns over finite timescales. Here, we study brain wave patterning in different physiological contexts using two independent approaches: The first is based on quantifying stochasticity relative to the underlying mean behavior, and the second assesses "orderliness" of the waves' features. The corresponding measures capture the waves' characteristics and abnormal behaviors, such as atypical periodicity or excessive clustering, and demonstrate coupling between the patterns' dynamics and the animal's location, speed, and acceleration. Specifically, we studied patterns of θ, γ, and ripple waves recorded in mice hippocampi and observed speed-modulated changes of the wave's cadence, an antiphase relationship between orderliness and acceleration, as well as spatial selectiveness of patterns. Taken together, our results offer a complementary-mesoscale-perspective on brain wave structure, dynamics, and functionality.

A Brain-Inspired Model of Hippocampal Spatial Cognition Based on a Memory-Replay Mechanism

Since the hippocampus plays an important role in memory and spatial cognition, the study of spatial computation models inspired by the hippocampus has attracted much attention. This study relies mainly on reward signals for learning environments and planning paths. As reward signals in a complex or large-scale environment attenuate sharply, the spatial cognition and path planning performance of such models will decrease clearly as a result. Aiming to solve this problem, we present a brain-inspired mechanism, a Memory-Replay Mechanism, that is inspired by the reactivation function of place cells in the hippocampus. We classify the path memory according to the reward information and find the overlapping place cells in different categories of path memory to segment and reconstruct the memory to form a “virtual path”, replaying the memory by associating the reward information. We conducted a series of navigation experiments in a simple environment called a Morris water maze (MWM) and in a complex environment, and we compared our model with a reinforcement learning model and other brain-inspired models. The experimental results show that under the same conditions, our model has a higher rate of environmental exploration and more stable signal transmission, and the average reward obtained under stable conditions was 14.12% higher than RL with random-experience replay. Our model also shows good performance in complex maze environments where signals are easily attenuated. Moreover, the performance of our model at bifurcations is consistent with neurophysiological studies.

Optimism and pessimism in optimised replay

The replay of task-relevant trajectories is known to contribute to memory consolidation and improved task performance. A wide variety of experimental data show that the content of replayed sequences is highly specific and can be modulated by reward as well as other prominent task variables. However, the rules governing the choice of sequences to be replayed still remain poorly understood. One recent theoretical suggestion is that the prioritization of replay experiences in decision-making problems is based on their effect on the choice of action. We show that this implies that subjects should replay sub-optimal actions that they dysfunctionally choose rather than optimal ones, when, by being forgetful, they experience large amounts of uncertainty in their internal models of the world. We use this to account for recent experimental data demonstrating exactly pessimal replay, fitting model parameters to the individual subjects’ choices.

When animals are asleep or restfully awake, populations of neurons in their brains recapitulate activity associated with extended behaviourally-relevant experiences. This process is called replay, and it has been established for a long time in rodents, and very recently in humans, to be important for good performance in decision-making tasks. The specific experiences which are replayed during those epochs follow highly ordered patterns, but the mechanisms which establish their priority are still not fully understood. One promising theoretical suggestion is that each replay experience is chosen in such a way that the learning that ensues is most helpful for the subsequent performance of the animal. A very recent study reported a surprising result that humans who achieved high performance in a planning task tended to replay actions they found to be sub-optimal, and that this was associated with a useful deprecation of those actions in subsequent performance. In this study, we examine the nature of this pessimized form of replay and show that it is exactly appropriate for forgetful agents. We analyse the role of forgetting for replay choices of our model, and verify our predictions using human subject data.

Spatial representability of neuronal activity

A common approach to interpreting spiking activity is based on identifying the firing fields—regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at preferred locations in the navigated environment, head direction cells that fire at preferred orientations of the animal’s head, view cells that respond to preferred spots in the visual field, etc. In all these cases, firing fields were discovered empirically, by trial and error. We argue that the existence and a number of properties of the firing fields can be established theoretically, through topological analyses of the neuronal spiking activity. In particular, we use Leray criterion powered by persistent homology theory, Eckhoff conditions and Region Connection Calculus to verify consistency of neuronal responses with a single coherent representation of space.

Evaluating State Space Discovery by Persistent Cohomology in the Spatial Representation System

Persistent cohomology is a powerful technique for discovering topological structure in data. Strategies for its use in neuroscience are still undergoing development. We comprehensively and rigorously assess its performance in simulated neural recordings of the brain's spatial representation system. Grid, head direction, and conjunctive cell populations each span low-dimensional topological structures embedded in high-dimensional neural activity space. We evaluate the ability for persistent cohomology to discover these structures for different dataset dimensions, variations in spatial tuning, and forms of noise. We quantify its ability to decode simulated animal trajectories contained within these topological structures. We also identify regimes under which mixtures of populations form product topologies that can be detected. Our results reveal how dataset parameters affect the success of topological discovery and suggest principles for applying persistent cohomology, as well as persistent homology, to experimental neural recordings.

From Topological Analyses to Functional Modeling: The Case of Hippocampus

Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.

Editorial: Topological Neuroscience

Topology, in its many forms, describes relations. It has thus long been a central concept in neuroscience, capturing structural and functional aspects of the organization of the nervous system and their links to cognition. Recent advances in computational topology have extended the breadth and depth of topological descriptions. This Focus Feature offers a unified overview of the emerging field of topological neuroscience and of its applications across the many scales of the nervous system from macro-, over meso-, to microscales.